A device of this kind is already known from U.S. Pat. No. 3,881,466. This device comprises a row of acoustic transducers whereby acoustic waves can be generated and received. Using a control circuit, each time different groups of neighbouring acoustic transducers are successively briefly pulsed in order to produce an acoustic beam, the acoustic echo pulses each time arriving being measured, thus scanning the body. In an electronic unit these acoustic echo pulses can be used to reconstruct an image of a cross-section of the body in that, for example, the measured acoustic echo pulses are reproduced as a brightness distribution in a plane after an analog treatment depending on the location of the relevant receiver and in accordance with their delay time, the brightness being dependent on the amplitude of the acoustic echo pulses. Devices of this kind are customarily referred to as B-scan devices. However, they offer only approximately true information as regards the position of acoustic interfaces in the body part exposed to the acoustic waves, because only those interfaces are recorded which reflect towards the transmitter, or which are situated at least approximately perpendicularly to the emission direction. Furthermore, it is not possible to determine the magnitude and the sign of an impedance gradient at an interface. The determination of the position of an interface is also inaccurate, because the reconstruction is based on a constant velocity of the sound and this is only approximately true. The inaccuracy is further increased in that first of all parallel acoustic waves are also liable to cross one another, so that "left" and "right" are interchanged. Moreover, multiple echos are also processed, so that in certain circumstances images of non-existent interfaces are actually formed.